Non-self Ćirić α+(θ, ϕ)-proximal contractions with best proximity point

Abstract

This study aims to provide a new class of Ćirić α+(θ, ϕ)-proximal contraction, a non-self generalized poximal contraction mapping on a non-empty closed subset of any metric space. Also we have proved that such contractions satisfying some conditions must have unique best proximity point if we take the base space as complete. For some particular values of the constants, that we have used to generalize the proximal contraction, we conclude different types of proximal contractions with proof, that all such type of contractions must have unique best proximity point. Mathematics Subject Classification (2010). Primary 47H10, 54H25; Secondary 41A65, 46B20, 47H05, 47H09.